Re: does a matrix equivalent of the Arg function exist?

• To: mathgroup at smc.vnet.net
• Subject: [mg53601] Re: does a matrix equivalent of the Arg function exist?
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Thu, 20 Jan 2005 03:47:42 -0500 (EST)
• Organization: Uni Leipzig
• References: <csl1af\$6su\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

at least quaternions have a representation with angle and a 3d vector,
but you can always define more than a single angle and for quaternions
you may describe the 3d vector by the absolute value and the two angles
of spherical coordinates, i.e.

q={r*Cos[psi],r*Sin[psi]*Cos[phi]*Sin[theta],r*Sin[psi]*Sin[phi]*Sin[theta],r*Sin[psi]*Cos[theta]}

Regards
Jens

"Roger Bagula" <tftn at earthlink.net> schrieb im Newsbeitrag
news:csl1af\$6su\$1 at smc.vnet.net...
> Arg[x+I*y] exists for any complex number.
> The 2by2 Matrix:
> {{x,-y},{y,x}}
> behaves very much like the complex number.
> With Euler matrices being three rotations by angles such that a total
> angle exists,
> it seems that an angle equivalency function like Arg should exist
> generally for nbyn matrices as a kind of measure like the determinant.
> Has anyone heard of such a matrix measure?
> Any ideas about how to form such a function?
> It would be useful geometrically in things like space and point groups
> used in
> crystalography and spectra of molecules.
> --
> Respectfully, Roger L. Bagula